Mean, Median, and Mode

The Mean of a Data Set

The mean of a set of numbers, sometimes simply called
the average
, is the sum of the data divided by the total number of data.

Example 1
:

Find the mean of the set
{
2
,
5
,
5
,
6
,
8
,
8
,
9
,
11
}
.

There are
8
numbers in the set. Add them all, and then divide by
8
.

2
+
5
+
5
+
6
+
8
+
8
+
9
+
11
8
=
54
8
=
6.75

So, the mean is
6.75
.

The Median of a Data Set

The median of a set of numbers is the middle number in the set (after the numbers have been arranged from least to greatest) -- or, if there are an even number of data, the median is the average of the middle two numbers.

Example 1
:

Find the median of the set
{
2
,
5
,
8
,
11
,
16
,
21
,
30
}
.

There are
7
numbers in the set, and they are arranged in ascending order. The middle number (the
4
th one in the list) is
11
. So, the median is
11
.

Example 2
:

Find the median of the set
{
3
,
10
,
36
,
255
,
79
,
24
,
5
,
8
}
.

First, arrange the numbers in ascending order.

{
3
,
5
,
8
,
10
,
24
,
36
,
79
,
255
}

There are
8
numbers in the set -- an even number. So, find the average of the middle two numbers,
10
and
24
.